With something as relatively simple a a radio, unless it's some hypersensitive unit you can probably have it work fine, but bear in mind that you will be slighly overstressing the electronics and this may lead to a somewhat shortened life over time. If it's an expensive radio I'd just get the rright adapter. If it's a cheapie live dangerously.

Very likely Not OK to use. It's possible the manufacturer built the radio of robust components that can handle an over voltage, but I wouldn't count on it. You're not likely to start a fire with those kinds of voltages and amperages, but you are likely to burn out a few components in the radio as they attempt to handle more current than they were built for. At the very least, the components will run hotter than they should and will shorten the life of your new gadget.

Tough call. Some things can tolerate a fair amount of overvoltage, though they may run hotter than normal. Other devices have voltage regulators and can tolerate quite a large range of input voltage with no adverse effects, other than a hot regulator, if the voltage is towards the high end. Many less expensive devices, however, will be destroyed by even a small excess voltage. So, while you might be able to get away with it, you should probably wait to get the correct adaptor. Knowing the risks, you may choose to try it, but realize that there's a chance you'll destroy your radio.

If you're going to buy an adapter anyway, you may want to consider a universal adapter that has multiple ends, and allows you to manually select the polarity and voltage. They're very handy to have around.

...you may want to consider a universal adapter that has multiple ends...

I've always liked the idea of these but I've never had one last longer than a few months. They just kinda stop working.

As for the OP, while others here have expressed the usual caution, I'd use the 11v one you have without any worries. Often, those rated adapter voltages are "very nominal" meaning pretty rough as accuracy goes. They are usually unregulated and may have different voltages for different loads. For example, it may measure 10.0volts with the tuner and volume turned low and 8.5volts at high volume and using the cassette motor.

If your universal adapters are malfunctioning, check the stats on them.
Mine worked great for years, until I tried to use it to power a small printer last month. That's when I noticed that the incredibly tiny print on the printer said 1.1A, wheras the adapter was rated for 500mA. Whoops!

I wouldn't feel good using a too-small amperage adapter (likely to overheat), but I'd go overvoltage by 2V at 9V without much worry. If you've got a multimeter you'll notice that, especially with no load, adapters don't jive 100% with their rated stats. The people making the hardware would certainly expect that.

Let’s assume the radio employs a 7806 6V regulator w/ TO-220 package. A TO-220 package typically has a RJC of 5 °C/W and a RCA of 65 °C/W. If we assume a 9V/600 mA (unregulated) wallwart has an output voltage of 9V, and if we assume the current draw is 600 mA, then the regulator would dissipate 1.8 W and the junction temperature would be 161 °C when the ambient temperature is 35 °C. This exceeds the 150 °C limit typically specified for 78XX regulators. Therefore, I would bet the 7806 regulator in the radio has a heat sink attached to it.

So what’s the RCA with the heat sink? Without knowing the particular heat sink that’s being used it’s impossible to know. Lets assume RCA = 20 °C/W when the heat sink is used, and thus the overall thermal resistance is 25 °C/W.

If we use a 9V/600 mA wallwart, and we (again) assume an ambient temperature of 35 °C, the power dissipation would be 1.8 W and the junction temperature would be 80 °C. This is O.K. given the 150 °C limit typically specified for 78XX regulators.

If we use a 11V/600 mA wallwart, the power dissipation would be 3 W and the junction temperature would be 110 °C, which is a temperature increase of a whopping 30 °C. Even though it’s within the 150 °C limit typically specified for 78XX regulators, this temperature rise would make me uncomfortable. Besides, how do you know the wallwart’s output voltage will be 11V? Because most wallwarts are unregulated, the output voltage could be significantly higher than the nominal rated voltage, especially if you draw a lot less current than the maximum (which may not be the case in your situation). But just to be safe, let’s assume the 11V/600 mA wallwart has an output voltage of 12 V. This will make the junction temperature 125 °C, which (in my opinion) is too close for comfort.

BTW: If we assume the radio uses a 5 V regulator the situation is even worse. This is another reason for going with the right wallwart. On the other hand, if the radio uses a switching regulator then (for the most part) all of this was a waste of time.

Anyway, the message here is that you should use a 9V wallwart. Mouser Electronics sells them real cheap.